It is a circle with a twelve-mile radius, with the center of the circle in the center of the town of New Castle, Delaware. In 1750, the center of the circle was fixed at the cupola of the courthouse in New Castle. The Twelve-Mile Circle continues into the Delaware River. A small portion of the circle, known as the "Arc Line," also forms part of the Mason-Dixon line, separating Delaware and Maryland. The Twelve-Mile Circle is the only territorial boundary in the United States that is a true arc (excluding all boundaries defined by latitude and longitude, like much of the border between the US and Canada, which—when viewed with the North Pole as the center—are all also arcs).
all that the Towne of Newcastle otherwise called Delaware and All that Tract of Land lying within the Compass or Circle of Twelve Miles about the same scituate lying and being upon the River Delaware in America And all Islands in the same River Delaware and the said River and Soyle thereof lying North of the Southermost part of the said Circle of Twelve Miles about the said Towne.
The fact that the circle extends into the Delaware River makes for an unusual territorial possession. Most territorial boundaries that follow watercourses split the water course between the two territories by one of two methods, either by the midpoint of the watercourse (the Grotian Method, after Hugo Grotius) or, more often, midpoint of the main flow channel, or thalweg. However, due to the text of the deed, within the Twelve-Mile Circle, all the Delaware River to the low-tide mark on the east (New Jersey) side is territory of the state of Delaware.
New Jersey has often debated this claim, as the rest of its territorial boundaries along the Delaware River are determined by the Thalweg method. The dispute has been brought to the Supreme Court of the United States on three occasions (all titled New Jersey v. Delaware), most notably in 1934, and also in 1935 and 2007. The court's opinion for the first case contains an extensive history of the claims to this territory, and the second memorably enjoins New Jersey and Delaware from ever disputing their jurisdictions again.
Regardless of the Supreme Court's admonition to the two states against further litigation on this subject, they were back before the court as late as November 2005, when New Jersey's desire to approve plans by BP to build a liquefied natural gas terminal along the New Jersey shore of the Delaware River fell afoul of Delaware's Coastal Zone Act. The court on January 23, 2006, appointed a special master to study the border dispute, a process likely to take years. Meanwhile the Delaware House of Representatives considered a (symbolic) bill to call out the National Guard to safeguard the State's interests, while New Jersey legislators made comments about the Battleship New Jersey, moored upriver from the site.